Sarah Zerbini

Multi-scale Analysis of MEMS Sensors Subject to Drop Impacts

The effect of accidental drops on MEMS sensors are examined within the framework of a multi-scale finite element approach. With specific reference to a polysilicon MEMS accelerometer supported by a naked die, the analysis is decoupled into macro-scale (at die length-scale) and meso-scale (at MEMS length-scale) simulations, accounting for the very small inertial contribution of the sensor to the overall dynamics of the device. Macro-scale analyses are adopted to get insights into the link between shock waves caused by the impact against a target surface and propagating inside the die, and the displacement/acceleration histories at the MEMS anchor points. Meso-scale analyses are adopted to detect the most stressed details of the sensor and to assess whether the impact can lead to possible localized failures. Numerical results show that the acceleration at sensor anchors cannot be considered an objective indicator for drop severity. Instead, accurate analyses at sensor level are necessary to establish how MEMS can fail because of drops.

Modeling Impact-induced Failure of Polysilicon MEMS: A Multi-scale Approach

Failure of packaged polysilicon micro-electro-mechanical systems (MEMS) subjected to impacts involves phenomena occurring at several length-scales. In this paper we present a multi-scale finite element approach to properly allow for: (i) the propagation of stress waves inside the package; (ii) the dynamics of the whole MEMS; (iii) the spreading of micro-cracking in the failing part(s) of the sensor. Through Monte Carlo simulations, some effects of polysilicon micro-structure on the failure mode are elucidated.

Multi-scale analysis of polysilicon MEMS sensors subject to accidental drops: Effect of packaging.

Abstract The effect of packaging on the impact-carrying capacity of micro electro-mechanical systems (MEMS) is investigated, with specific reference to a translational accelerometer. By exploiting the small ratio between the masses of MEMS and package/die (typically 10 − 3 or less) a decoupled two-scale, finite element approach is adopted: at the package/die length-scale the dynamics of whole device after the impact against a flat target surface is studied; at the sensor length-scale the response of the MEMS to the drop-induced loading is investigated, and MEMS details where the stress state can exceed the tensile strength of polysilicon are identified. Two drop orientations are considered, here termed bottom and top; in the first case, package and die strike the target with their bottom surfaces; in the second case, they fall upside-down, and strike the target with their top surfaces. By comparing the simulation outcomes in terms of maximum attained tensile stress, it results that package does not always lead to benefits in term of capability of the studied sensor to sustain drops. In the bottom drop configuration, e.g. MEMS failure may be triggered by the package.

Optical detection of the Coriolis force on a silicon micromachined gyroscope

In this paper, we report on the optical characterization of a micromachined gyroscope prototype for automotive applications, by means of feedback interferometry. In order to directly detect the rotation-induced Coriolis force, we have developed a compact and stable interferometric setup, which has been positioned inside a small vacuum bell, mounted on a rotating table. By this setup, which has a noise limit of the order of 10/sup -11/ m/(Hz)/sup 1/2/, we have measured the gyro responsivity curve, demonstrating the feasibility of the optical interferometric detection of the in-plane response of a MEMS sensor. In addition, we have carried out the full mechanical characterization of the device at different pressures, and we have performed the matching of the gyro resonance frequencies by the interferometric monitoring. Our gyro had a resonance frequency of 3986 Hz for both axes after tuning; at a pressure of 7 10/sup -2/ torr, the quality factor were Q=18000 for the driving axis and Q=1800 for the sensing axis, while the measured responsivity was 7 10/sup -10/ m/(/spl deg//s). The optical characterization represents an important feedback to the designer and is especially powerful in the case of prototypes for which the on-board electronics is not yet available.

Optimization of Sensing Stators in Capacitive MEMS Operating at Resonance

This paper describes capacitive sensing stators for microelectromechanical systems (MEMS) suitably designed to minimize damping effects without worsening the capacitive variation per unit displacement. Such optimization can be exploited to maximize the readout signal in resonant systems. Two structures are designed with the aid of finite-element method models for the electrostatic domain, and with the aid of a deterministic integral model for damping predictions. The structures, fabricated in a 22-μm-thick surface micromachining process, demonstrate a 3× sensitivity improvement when used as resonant MEMS magnetometers.

Dynamic nonlinear behavior of torsional resonators in MEMS

This paper reports the theoretical and experimental characterization of the dynamic behavior of torsional resonators that can be applied to inertial sensors. For the correct operation of the devices it is necessary to model the dynamic behavior of the electrostatically actuated torsional resonators both in the linear and nonlinear range. A complete analytical model is developed in this work including nonlinear terms in the electrostatic stiffness. This provides clear quantitative information about the available linear range of operation and opens the way to exploit the nonlinear range. The model is validated through comparison with experimental data on two 22 µm thick polysilicon resonators having different distances from the underlying electrodes.

Single-Structure Micromachined Three-Axis Gyroscope With Reduced Drive-Force Coupling

This letter presents a micromachined silicon three-axis gyroscope based on a triple tuning-fork structure utilizing a single vibrating element. The mechanical approach proposed in this letter uses a secondary “auxiliary” mass rather than a major “proof” mass to induce motion in the proof mass frame for Coriolis force coupling to the sense mode. These auxiliary masses reduce the unwanted mechanical coupling of force and motion from the drive mode to the three sense modes. The experimental data show that the bias error due to coupling is reduced by a factor up to 10, and the bias instability of each sense axis is reduced by a factor of up to 3 when the gyroscope is actuated using the auxiliary masses rather than the major masses. The gyroscope exhibits a bias instability of 0.016°/s, 0.004°/s, and 0.043°/s for the x-, y-, and z-sense modes, respectively. Furthermore, initial temperature characterization results show that the gyroscope actuated by the auxiliary masses ensures a better bias instability performance in each sense axis over a temperature range from 10 °C to 50 °C in comparison with the gyroscope actuated by the major masses.

Sensitivity and temperature behavior of a novel z-axis differential resonant micro accelerometer

The present work concerns the operating principle and a thorough experimental characterization of a new polysilicon resonant micro accelerometer for out-of-plane measurements, fabricated using an industrial surface micromachining technique. This device is characterized by differential resonant sensing, obtained from the variation of the electrostatic stiffness of two torsional resonators under the application of an external acceleration. The sensitivity, defined as the differential shift in resonance frequencies per gravity unit (lg = 9.8 m s−2), is of about 10 Hz g−1when operated at a DC bias of 1.5 V only. Over an acceleration range larger than 10 g, the deviation from linearity is lower than 1% and the cross-axis rejection is larger than 34 dB. The resonators temperature coefficients of frequency, in the order of −29 ppm C−1, are matched within about 0.1%, resulting in linear offset drifts against temperature lower than 5 mg up to 95 C in absence of any digital compensation.

Physically-based reduced order modelling of a uni-axial polysilicon MEMS accelerometer.

In this paper, the mechanical response of a commercial off-the-shelf, uni-axial polysilicon MEMS accelerometer subject to drops is numerically investigated. To speed up the calculations, a simplified physically-based (beams and plate), two degrees of freedom model of the movable parts of the sensor is adopted. The capability and the accuracy of the model are assessed against three-dimensional finite element simulations, and against outcomes of experiments on instrumented samples. It is shown that the reduced order model provides accurate outcomes as for the system dynamics. To also get rather accurate results in terms of stress fields within regions that are prone to fail upon high-g shocks, a correction factor is proposed by accounting for the local stress amplification induced by re-entrant corners.

Multi-Scale Modeling of Shock-Induced Failure of Polysilicon MEMS

We investigate the shock-induced stress state and possible failure mechanisms in polysilicon MEMS sensors. In case of accidental drop events, we aim at highlighting the links between drop features, like drop height and impact angles, and the location of the failing detail of the device. Taking into account the small inertial contribution of the sensor to the whole package dynamics, we adopt a decoupled multi-scale numerical approach, where macro-scale analyses (at die length-scale) are used to define the acceleration records to be adopted as loading in meso-scale (at sensor length-scale) simulations. We show that a commonly adopted indicator to assess drop severity is not able to take in due account the details of the impact event and possible very localized failures at the sensor level.